The Journal of the Indian Mathematical Society

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Nc-Pure Regular Near-rings


Affiliations
1 Department of Mathematics, Annamalai University, Annamalainagar-608 002, India
2 Department of Mathematics (DDE), Annamalai University, Annamalainagar-608 002, India
     

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In this paper we introduce the notion of Nc-pwe and strict Nc-pure near-rings. We have shown that a reduced near-ring N with identity is Nc-pure if and only if whenever e < a for some e ∉ Nc and ∈ N implies e = ea = and a - e is an idempotent element. We have also obtained an equivalent condition for a Nc pure near-ring to be strict Ncpure.
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  • Nc-Pure Regular Near-rings

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Authors

P. Dheena
Department of Mathematics, Annamalai University, Annamalainagar-608 002, India
D. Sivakumar
Department of Mathematics (DDE), Annamalai University, Annamalainagar-608 002, India

Abstract


In this paper we introduce the notion of Nc-pwe and strict Nc-pure near-rings. We have shown that a reduced near-ring N with identity is Nc-pure if and only if whenever e < a for some e ∉ Nc and ∈ N implies e = ea = and a - e is an idempotent element. We have also obtained an equivalent condition for a Nc pure near-ring to be strict Ncpure.